Simplification Questions

FACTS  AND  FORMULAE  FOR  SIMPLIFICATION  QUESTIONS

 

 

1. BODMAS Rule: This rule depicts the correct sequence in which the operations are to be executed,so as to find out the value of a given expression. Here, 'B' stands for bracket , 'O' for of , 'D' for division and 'M' for multiplication, 'A' for addition and 'S' for subtraction.

Thus, in simplifying an expression, first of all the brackets must be removed, strictly in the order(), {} and [].

After removing the brackets, we must use the following operations strictly in the order:

(1) of    (2)division   (3) multiplication   (4)addition   (5)subtraction.

 Modulus of a real number : Modulus of a real number a is defined as |a| = aif a>0-aif a<0

 

2. Virnaculum (or bar) : When an expression contains Virnaculum, before applying the ‘BODMAS’ rule, we simplify the expression under the Virnaculum.

Q:

Simplify the fraction?

5 (2/7) - 3 (1/14) - 2 (1/14) - 1 (1/7) = ? + 3 (1/17) 

A) -4 (1/17) B) 5 (2/17)
C) -2 (1/17) D) 3 (3/17)
 
Answer & Explanation Answer: A) -4 (1/17)

Explanation:

Given fraction is 5 (2/7) - 3 (1/14) - 2 (1/14) - 1 (1/7) = ? + 3 (1/17) 

It can be written as 

(5 - 3 - 2 - 1) + (2/7 - 1/14 - 1/14 - 1/7) = ? +  3 (1/17) 

-1 + 0 - 3 (1/17) = ?

=> ? = -4 (1/17)

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Q:

If a+b=5 and 3a+2b=20,then (3a+b)will be :

 

A) 20 B) 15
C) 25 D) 30
 
Answer & Explanation Answer: C) 25

Explanation:

a+b=5   ...(1)    and    3a+2b=20 ...(2)

 

Multiplying (1) by 2 and subtracting from (2), we get : a=10.

 

Putting a=10 in (1), we get : b=-5

 

Therefore,   (3a+b) = 3 x 10+(-5)=30-5=25.

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Q:

Simplify the following equation.

1943 + 12 + 13 + 11 + 14

A) 43/19 B) 1
C) 38/19 D) None of these
 
Answer & Explanation Answer: D) None of these

Explanation:

After solving we get,

 

62/931.

 

None of the options satisfy.

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Q:

Simplify and find '?'

48?+32? = 320

A) 4 B) 8
C) 16 D) 32
 
Answer & Explanation Answer: C) 16

Explanation:

given

 48?+32?= 320 

=> 6?+4?=40

Now squaring on both sides

=> 36 x ? + 16 x ? + 48 x ? = 1600

=> 100 x ? = 1600

=>  ? = 16

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14 29246
Q:

In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?

A) 160 B) 175
C) 180 D) 195
 
Answer & Explanation Answer: B) 175

Explanation:

Suppose the man works overtime for x hours.

Now, working hours in 4 weeks = (5 x 8 x 4) = 160.

Therefore,  160 * 2.40 + x * 3.20 = 432

 => 3.20x = 432 - 384 = 48

 => x = 15.

 Hence, total hours of work = (160 + 15) = 175.

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34 28825
Q:

If a + b + c = 13, a2+b2+c2=69 then find the ab + bc + ca :

A) 10 B) 30
C) 50 D) 70
 
Answer & Explanation Answer: C) 50

Explanation:

a+b+c2=a2+b2+c2+2ab+bc+ca

2ab+bc+ca=a+b+c2-a2+b2+c2=169-69=100=ab+bc+ca=50

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Q:

Simplify the following equation

[K-L2-K+L2]4K = a/b

A) K = b /a B) bL = -a
C) KL = 1 D) aK = -b
 
Answer & Explanation Answer: B) bL = -a

Explanation:

[(K-L)2-K+L2]4K = abK2+L2-2KL-K2+L2+2KL4K= ab

 

=> - 4KL/4K = a/b

 

=> L = - a/b

 

=> bL = -a

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Q:

1397 x 1397 = ?

Here what replaces '?' 

A) 1951609 B) 1821504
C) 2031489 D) 1847879
 
Answer & Explanation Answer: A) 1951609

Explanation:

1397 x 1397

Number System mcq solution image

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